Before going
further, let us recall the concept of elasticity and elastic limit first. As we
have already discussed that if an external force is
applied over the object, there will be some deformation or changes in the shape
and size or simply dimensions of the object. Body will secure its original
shape and size after removal of external force if deformation due to external
force is within certain limit.

Therefore, there will be some specific
value of force for each material up to which, strain will be temporary or
elastic i.e. deformation will be disappeared after removal of load and
corresponding value of stress will be termed as elastic limit of that material.

According to Hook’s law

Within elastic limit, stress applied
over an elastic material will be directionally proportional to the strain
produced due to external loading. Mathematically we can say as displayed here
in figure.

Let us remove the proportionality sign
and therefore we will have to use one constant value in order to remove the
proportionality sign.

Where E is basically Modulus of
elasticity or young modulus and we can define modulus of elasticity as the
ratio of stress to strain. Modulus of elasticity will have same unit as that
for stress because strain is unit less parameter and therefore modulus of
elasticity unit in S.I. system will be N/m2.

Let us draw here the curve between
stress and strain for an elastic material. Stress value is provided here at
Y-axis and strain value at X-axis. We may notice here that as stress value increases
strain value will also be increased and similarly strain value will be
decreased with decrease in stress value and we must note it here that this
relationship will be linear, as shown in curve, up to elastic limit.

Do you have any suggestion? please write in comment box.

Reference:

Strength of material, By R. K. Bansal

Image Courtesy: Google

We will see another important topic in the category
of strength of material.